The radiation from a relativistic source is beamed with a typical
beaming angle 1 / .
This implies that if the source that is
expanding radially with an ultra-relativistic speed a given
observer "sees" radiation only from a region that is within
-1 from
its line of sight to the source. If the radius
of the emitting region is R the observer will see radiation from
a region of size R /
. Since
is extremely large
during the GRB we observe emission only from a small fraction of
the emitting shell. It is possible, and even likely, that the
conditions within the small region that we observe will be
different from the average ones across the shell. This means that
the conditions that we infer won't reflect the true average
conditions within this particular GRB.

An interesting point related to the internal shocks (discussed
later) model in this context is the following. According to the
internal shocks model individual pulses are obtained by
collisions between individual shells. Here the inhomogeneity of
individual shells could be wiped out when the contributions of
different hot spots from different shells is added. Alternatively
the "inner engine" may produce a consistent angular pattern in
which the hot spot is in the same position in all shells and in
this case averaging won't lead to a cancellation of the patchy
shell structure.

Within the internal-external model the GRB is produced by internal
shocks in which only the relative motion within the flow is
dissipated. The bulk Lorentz factor remains unchanged. During the
afterglow the shell is slowed down by external shocks. As the
Lorentz factor decreases with time (see Eq. 78) we
observe a larger and larger fraction of the emitting region until
-1, where
is the angular size
of the whole emitting region - the GRB jet, see
Section VIIH. This has several inevitable
implications. If the
initial relativistic flow is inhomogenous on a small angular scale
then different observers looking at the same GRB (from different
viewing angles) will see different
-rays light
curves. A strong
burst to one observer might look weak to another one if it is
located at an angle larger than 1 /
from the first. The two
observers will see similar conditions later on, during the
afterglow, as then they will observe the same angular regions.
This has the following implications: (i) Given that the GRB
population originate from some `typical' distribution we expect
that fluctuation between different bursts at early time during the
GRB will be larger than fluctuations observed at late times during
the afterglow
[206].
A direct consequence of this behaviour
is the appearance of a bias in the observations of GRBs. As we are
more likely to detect stronger events we will tend to identify
bursts in which a `hot spot` was pointing towards us during the
GRB phase. If the original GRB shells are inhomogenous this would
inevitably lead to a bias in the estimates of the GRB emission as
compared to the kinetic energy during the afterglow. (ii) As the
afterglow slows down we observe a larger and larger region. The
angular structure would produces a variability in the light curve
with a typical time scale of t, the observed time. These
fluctuations will decay later as the Lorentz factor decreases and
the observations are averaged over a larger viewing angle.
Nakar et al.
[274]
have suggested that this is the
source of the early fluctuations in the light curve of GRB 021004. Nakar and Oren
[267]
modelled this process with a numerical
simulation. They find that the flucutation light curve of
GRB 021004 can be nicely fitted by this model and
that it also
explains the correlated fluctuations in the polarization (see also
[133]).